Approximate Analytical Solutions For Pipe Flow Of A Third Grade Fluid With Variable Models Of Viscosities And Heat Generation/ Absorption

Abstract

We study a one-dimensional heat generation and viscous dissipation model of a third grade fluid in a cylinder involving viscosities Reynold’s and a Vogel’s. The analysis is based on regular perturbation technique. Approximate analytical expressions are constructed for the dimensionless velocity and temperature fields. The heat transfer model is also numerically simulated. The present numerical solutions agree very well with the previous finite difference scheme for special cases. The new analytical solutions are compared with numerical integration and with relative error of 5 % for all physical parameters, an excellent agreement is observed. In particular, in the absence of heat generation/absorption case δ = 0, we recover earlier known analytical results. Then, if δ =/= 0, the effects of several dimensionless parameters on the heat transfer characteristics are reported graphically to elucidate special features of the solutions.